Although I can't tell you if there would be a deficiency in a fruit-only diet...this article compares differences in a few of the essentials that a child would need. Iron ,Fiber, Folate, Vit C, Calcium etc. The writer uses data to compare the amount of nutrients in certain vegetables vs fruits and at least from her selection; the vegetables wins hands in nutrients compared to the same amount of servings in fruit.
https://scienceofmom.com/2011/12/22/fruits-vs-veggies-are-they-nutritionally-equivalent/
If anything, the imbalance would be too much sugar from the fruit. Don't give up on the vegetables! there's got to be something that they find a liking to.